A plane has all of its 100 seats booked for the next flight. When the boarding starts, the first passenger to enter the plane is drunk, and sits on a random seat.
After that, the remaining passengers enter the plane one by one, and sit on their seat if it’s free, or on a random one if their own place is occupied. What is the probability that the last passenger sits on the correct seat?
Solution
The simplest way to approach this problem is to observe that by the time the last passenger enters the plane, the seats belonging to passengers 2 to 99 are occupied. Therefore, the last passenger can only end up seated on their own seat, or on the drunk passenger’s seat. From the perspective of the first 99 passengers, these two seats are identical, and thus there is a 50% chance that the last passenger sits on the correct seat.
